The Palestinian president, Mahmoud Abbas, has convened a meeting of the Palestinian leadership in Ramallah amid mounting speculation about an imminent breakthrough in US efforts to persuade both sides of the Israeli-Palestinian conflict to return to the negotiating table.

Abbas will report on his latest meetings with the US secretary of state, John Kerry, in Amman this week and confer with leaders of the Palestine Liberation Organisation and the main political factions on proposals for the resumption of talks.

Israel's president Shimon Peres further raised expectations in a statement which said: "From the latest information at my disposal, Secretary Kerry has succeeded in progressing the chance for opening peace talks.... The coming days are crucial and we are within touching distance." Both parties, he added, were "making an effort to overcome the final obstacles".

Thursday's meeting of the Palestinian leadership follows a statement issued by Arab League diplomats in Amman on Wednesday endorsing new negotiations, and an assessment by Kerry that the gaps between the two sides had significantly narrowed.

"Through hard and deliberate work, we have been able to narrow those gaps very significantly," Kerry told a press conference. "We continue to get closer and I continue to be hopeful that the two sides will come to sit at the same table."

However, he added: "There is still some language that needs to be worked out".

An Arab League statement said: "The Arab delegates believe Kerry's ideas ... constitute a good ground and suitable environment for restarting the negotiations." It added that "any future deal must be based on a two-state solution and through establishing an independent Palestinian state on the 4 June 1967 borders with a limited exchange of lands in the same value and size."

The Palestinians' insistence on the 1967 border as the basis for any territorial agreement has been one of the key sticking points during Kerry's six visits to the region since March. Israel says it is unwilling to concede territory before negotiations begin.

The Palestinians also want the release of around 100 long-term prisoners and a freeze on settlement construction. The Israeli prime minister, Binyamin Netanyahu, is believed to have agreed to a limited prisoner release, and an informal moratorium on building in settlements outside the major blocks close to the 1967 line.

The Israeli defence minister on Wednesday postponed the approval of around 300 new homes in settlements deep inside the West Bank. But the construction of more than 700 homes in the settlement of Modi'in Ilit, close to the 1967 line, was given initial approval by the Civil Administration, the Israeli body which governs much of the West Bank.

Kerry has so far met only with Palestinian negotiators during this week's visit to the region, suggesting – according to some analysts – that heavy diplomacy had already accomplished results on the Israeli side. However, some Israeli officials said that a directive to be issued by the European Union, which bars funding and co-operation to Israeli settlements, could adversely affect any progress.

Fears that Netanyahu may drag his feet once negotiations start were fuelled this week by an unidentified Israeli government minister saying the prime minister's primary objective was merely to show willingness to negotiate and that he did not intend to engage in a far-reaching peace process.

According to one western diplomat, the Palestinians were likely to insist on a tight timeframe and impartial refereeing by the Americans to prevent such a scenario.

Kerry has persisted in his mission to breathe new life into the moribund peace process in the face of deep scepticism on both sides. Netanyahu and Abbas have not met face to face for almost three years. Kerry, along with many others, has warned that time is running out for a peace deal which allows the Palestinians to establish a state of their own.